Estimating diffusivity along a reaction coordinate in the high friction limit: Insights on pulse times in laser-induced nucleation

Multiscale approach to the theory of nonisothermal homogeneous nucleation

Molecular dynamics (MD) of the Lennard-Jones cluster in the environment of supersaturated vapor at fixed temperature and density is used for the investigation of nonisothermal nucleation. The results allow one to single out different processes occurring at different time scales, the Ornstein-Uhlenbeck fluctuations at the short time scale and a combination of slow diffusion and drift of the fluctuation packet that represents a cluster, at the long time scale. The multiscale approach is developed, in which a separate treatment of different time scales makes it possible to consider strongly correlated cluster size and temperature. This reduces the nonisothermal cluster evolution to a one-dimensional problem. The fluctuation packet drift velocity and diffusivity are calculated based on the cluster microscopic thermophysical parameters determined in this work from MD data for isothermal clusters. The proposed approach is consistent with the results of our MD simulation.

A Review of Laser-Induced Crystallization from Solution

Crystallization abounds in nature and industrial practice. A plethora of indispensable products ranging from agrochemicals and pharmaceuticals to battery materials are produced in crystalline form in industrial practice. Yet, our control over the crystallization process across scales, from molecular to macroscopic, is far from complete. This bottleneck not only hinders our ability to engineer the properties of crystalline products essential for maintaining our quality of life but also hampers progress toward a sustainable circular economy in resource recovery. In recent years, approaches leveraging light fields have emerged as promising alternatives to manipulate crystallization. In this review article, we classify laser-induced crystallization approaches where light-material interactions are utilized to influence crystallization phenomena according to proposed underlying mechanisms and experimental setups. We discuss nonphotochemical laser-induced nucleation, high-intensity laser-induced nucleation, laser trapping-induced crystallization, and indirect methods in detail. Throughout the review, we highlight connections among these separately evolving subfields to encourage the interdisciplinary exchange of ideas.

Using optical tweezing to control phase separation and nucleation near a liquid-liquid critical point

About 20 years ago, it was shown that lasers can nucleate crystals in super-saturated solutions and might even be able to select the polymorph that crystallises. However, no theoretical model was found explaining the results and progress was slowed down. Here we show that laser-induced nucleation may be understood in terms of the harnessing of concentration fluctuations near a liquid-liquid critical point using optical tweezing in a process called laser-induced phase separation (LIPS) and LIPS and nucleation (LIPSaN). A theoretical model is presented based on the regular solution model with an added term representing optical tweezing while the dynamics are modelled using a Kramers diffusion equation, and the roles of heat diffusion and thermophoresis are evaluated. LIPS and LIPSaN experiments were carried out on a range of liquid mixtures and the results compared to theory.

Solubility curves and nucleation rates from molecular dynamics for polymorph prediction – moving beyond lattice energy minimization

Seeded nucleation simulations allow for the screening of low energy structures to predict final structure present in solution.

Transition-State Theory, Dynamics, and Narrow Time Scale Separation in the Rate-Promoting Vibrations Model of Enzyme Catalysis

The power of transition-state theory (TST) for understanding enzymes is evidenced by its recent use in the design and synthesis of highly active de novo enzymes. However, dynamics can influence reaction kinetics, and some studies of rate-promoting vibrations even claim that dynamical theories instead of TST are needed to understand enzymatic reaction mechanisms. For the rate-promoting vibration (RPV) model of enzyme catalysis [Antoniou et al., J. Chem. Phys. 2004, 121, 6442], a reactive flux correlation function analysis shows that dynamical effects do slow the kinetics. However, the RPV model also shows extremely long-lived correlations because the RPV and the bath are not directly coupled. Additionally, earlier studies of the RPV model show a narrow time scale separation due to a small 5kT barrier. Thus earlier findings based on the RPV model may have little bearing on the properties of real enzymes. The intrinsic reaction coordinate (IRC) reveals that the RPV is an important component of the reaction coordinate at early and late stages of the pathway, but the RPV is not an important component of the reaction coordinate direction at the transition state. The unstable eigenmode from harmonic TST (which coincides with the IRC at the saddle point) gives a larger transmission coefficient than the coordinate used in the correlation functions of Antoniou et al. Thus while TST cannot predict the transmission coefficient, the RPV model suggests that TST can provide mechanistic insights on elementary steps in enzyme catalysis. Finally, we propose a method for using the transition-state ensemble as predicted from harmonic TST to distinguish promoting vibrations from other more mundane bath variables.

A design equation for low dosage additives that accelerate nucleation

Additives are used to control nucleation in many natural and industrial environments. However, the mechanisms by which additives inhibit or accelerate solute precipitate nucleation are not well understood. We propose an equation that predicts changes in nucleation barriers based on the adsorption properties and concentrations of trace additives. The equation shows that nucleant efficacy depends on the product of an adsorption equilibrium constant and the reduction in interfacial tension. Moreover, the two factors that determine the potency of additives are related to each other, suggesting that assays of just one property might facilitate additive design. We test the design equation for a Potts lattice gas model with surfactant-like additives in addition to solutes and solvents.

Carbohydrate-protein interactions that drive processive polysaccharide translocation in enzymes revealed from a computational study of cellobiohydrolase processivity

Translocation of carbohydrate polymers through protein tunnels and clefts is a ubiquitous biochemical phenomenon in proteins such as polysaccharide synthases, glycoside hydrolases, and carbohydrate-binding modules. Although static snapshots of carbohydrate polymer binding in proteins have long been studied via crystallography and spectroscopy, the molecular details of polysaccharide chain processivity have not been elucidated. Here, we employ simulation to examine how a cellulose chain translocates by a disaccharide unit during the processive cycle of a glycoside hydrolase family 7 cellobiohydrolase. Our results demonstrate that these biologically and industrially important enzymes employ a two-step mechanism for chain threading to form a Michaelis complex and that the free energy barrier to chain threading is significantly lower than the hydrolysis barrier. Taken with previous studies, our findings suggest that the rate-limiting step in enzymatic cellulose degradation is the glycosylation reaction, not chain processivity. Based on the simulations, we find that strong electrostatic interactions with polar residues that are conserved in GH7 cellobiohydrolases, but not in GH7 endoglucanases, at the leading glucosyl ring provide the thermodynamic driving force for polysaccharide chain translocation. Also, we consider the role of aromatic-carbohydrate interactions, which are widespread in carbohydrate-active enzymes and have long been associated with processivity. Our analysis suggests that the primary role for these aromatic residues is to provide tunnel shape and guide the carbohydrate chain to the active site. More broadly, this work elucidates the role of common protein motifs found in carbohydrate-active enzymes that synthesize or depolymerize polysaccharides by chain translocation mechanisms coupled to catalysis.

Toward a molecular theory of homogeneous bubble nucleation: II. Calculation of the number density of critical nuclei and the rate of nucleation

In the present paper, we develop a method to calculate the rate of homogeneous bubble nucleation within a superheated L-J liquid based on the (n,v) equilibrium embryo free energy surface introduced in the first paper (DOI: 10.1021/jp404149n). We express the nucleation rate as the product of the concentration of critical nuclei within the metastable liquid phase and the relevant forward rate coefficient. We calculate the forward rate coefficient of the critical nuclei from their average lifetime as determined from MD simulations of a large number of embryo trajectories initiated from the transitional region of the metastable liquid configuration space. Therefore, the proposed rate coefficient does not rely on any predefined reaction coordinate. In our model, the critical nuclei belong to the region of the configuration space where the committor probability is about one-half, guaranteeing the dynamical relevance of the proposed embryos. One novel characteristic of our approach is that we define a limit for the configuration space of the equilibrium metastable phase and do not include the configurations that have zero committor probability in the nucleation free energy surface. Furthermore, in order to take into account the transitional degrees of freedom of the critical nuclei, we develop a simulation-based approach for rigorously mapping the free energy of the (n,v) equilibrium embryos to the concentration of the critical nuclei within the bulk metastable liquid phase.

Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency

We propose a method for identifying accurate reaction coordinates among a set of trial coordinates. The method applies to special cases where motion along the reaction coordinate follows a one-dimensional Smoluchowski equation. In these cases the reaction coordinate can predict its own short-time dynamical evolution, i.e., the dynamics projected from multiple dimensions onto the reaction coordinate depend only on the reaction coordinate itself. To test whether this property holds, we project an ensemble of short trajectory swarms onto trial coordinates and compare projections of individual swarms to projections of the ensemble of swarms. The comparison, quantified by the Kullback-Leibler divergence, is numerically performed for each isosurface of each trial coordinate. The ensemble of short dynamical trajectories is generated only once by sampling along an initial order parameter. The initial order parameter should separate the reactants and products with a free energy barrier, and distributions on isosurfaces of the initial parameter should be unimodal. The method is illustrated for three model free energy landscapes with anisotropic diffusion. Where exact coordinates can be obtained from Kramers-Langer-Berezhkovskii-Szabo theory, results from the new method agree with the exact results. We also examine characteristics of systems where the proposed method fails. We show how dynamical self-consistency is related (through the Chapman-Kolmogorov equation) to the earlier isocommittor criterion, which is based on longer paths.

Characterization of a dynamic string method for the construction of transition pathways in molecular reactions

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method.